Two-dimensionalSU(N)×SU(N)chiral models on the lattice. ii. the green's function

Analytical and numerical methods are applied to principal chiral models on a two-dimensional lattice and their predictions are tested and compared. New techniques for the strong coupling expansion of $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ models are developed and applied to the evaluation of the two-point correlation function. The momentum-space lattice propagator is constructed with precision $O\left({\beta }^{10}\right)$ and an evaluation of the correlation length is obtained for several different definitions. Three loop weak coupling contributions to the internal energy and to the lattice $\beta$ and $\gamma$ functions are evaluated for all $N$, and the effect of adopting the "energy" definition of temperature is computed with the same precision. Renormalization-group-improved predictions for the two-point Green's function in the weak coupling (continuum) regime are obtained and successfully compared with Monte Carlo data. We find that strong coupling is predictive up to a point where asymptotic scaling in the energy scheme is observed. Continuum physics is insensitive to the effects of the large $N$ phase transition occurring in the lattice model. Universality in $N$ is already well established for $N\gtrsim 10$ and the large $N$ physics is well described by a "hadronization" picture.